1. Section 2.5 Convex Polygons
A polygon is a closed plane figure whose sides are line segments that intersect only at the endpoints.
Convex polygons angles are between 0 and 180
Concave polygons have one angle that is more than 180 (reflex angle) Fig p. 99
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2. Types of Polygons Polygon Number of Sides Triangle 3 Quadrilateral 4
Pentagon 5
Hexagon 6
Heptagon 7
Octagon 8
Nonagon 9
Decagon 10
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3. Diagonals of a Polygon
Definition: a line segment that joins two nonconsecutive vertices.
Theorem 2.5.1: The total number of diagonals D in a polygon of n sides is given by the formula:
Polygon
Number of Diagonals
Triangle
Quadrilateral 2
Pentagon 5
Hexagon 9
Heptagon
? 14
Octagon
? 20
Nonagon
? 27
Decagon
? 35
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4. Sum of the Interior Angles of a Polygon
Sum of Interior Angles
Triangle
180
Quadrilateral
360
Pentagon
540
Hexagon
720
Heptagon
900 
Octagon
1080 
Nonagon
1260 
Decagon
1440 
Theorem 2.5.2: The sum S of the measures of the interior angles of a polygon with n sides is given by
S = (n-2) 180
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5. Regular Polygons A polygon that is both equilateral and equiangular
Corollary 2.5.3: The measure l of each interior angle of a regular polygon or equiangular polygon of n sides is:
Corollary 2.5.4: The sum of the four interior angles of a quadrilateral is 360.
Corollary 2.5.5: The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360. Proof p. 104
Corollary 2.5.6: The measure E of each exterior angle of a regular polygon or equiangular polygon in n sides is E = 360/n
Ex. 6 p. 104
Polygrams: Figure created when sides of a convex polygon are extended. Fig p. 109
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